Which of the following will provide the lowest amount of after-tax income for an individual in the top federal tax bracket?

Group of answer choices

$100 of eligible dividends from Canadian corporations

$100 of interest income from Canadian bonds

$100 of capital gains from Canadian stocks

$100 of non-eligible dividends from Canadian corporations

The weights of 2-year old children follow a normal distribution with an average weight of 26 lbs and a standard deviation of 1.5 lbs.

You select a random sample of 100 2-year old children.

What is the shape of the sampling distribution for the average of 100 2-year olds?

What is the mean of the sampling distribution for the average of 100 2-year olds?

What is the standard deviation of the sampling distribution for the average of 100 2-year olds?

Explain the 68-95-99.7 rule in this case (i.e. in what range you of values do you expect the average weight of 100 2-year olds to fall 68 %, 95%, 99.7% of the time (i.e. in many samples of size 100)? Show your calculations.

What is the probability that the average weight of 100 randomly selected 2-year olds is less than 26.04 lbs?

What is the probability that the average weight of 100 randomly selected 2-year olds is more than 26.04 lbs?

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Question: 1. In the following dataset you are given 48 observations on Quantity Demanded of Soda, Price of ...

1. In the following dataset you are given 48 observations on Quantity Demanded of Soda, Price of a six pack (in $) and temperature (degrees). Each row of data corresponds to a different market.

a. Perform a regression of Quantity Demanded on Price and Temperature. Recall, the instructions to do regression using Excel are in a word doc under the chapter 4 module.

Attach the regression output to your take home. Write down the equation for the sample regression equation using the coefficients from your regression output. Interpret the numerical coefficients of each of the X variables (discuss not just the sign but also the size of the coefficient).

b. Perform t tests of statistical significance for each of the X variables and interpret those t-tests in terms of the actual variables in the model) – do not just state statistically significant, or insignificant.

c. Assuming the average price and average temperature (they are listed in the last row of the dataset) calculate the own price elasticity of demand, Ep and the temperature elasticity of demand, Etemp.

d. Suppose this firm was to set the same price for its six packs of soda in each of its markets. What would be the revenue maximizing price? How many units of the good would the firm sell at the revenue maximizing price? What would the own price elasticity of demand be at this price?

e. Suppose that the average temperature is expected to increase by 5% this year. What would be the forecasted percentage change in demand?

You may need to use the appropriate technology to answer this question.

Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest).

(a)

The estimated regression equation for this data is

ŷ = 22.328 + 0.317x,

where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ = 0
H_a: β₁ ≠ 0H₀: β₁ ≥ 0
H_a: β₁ < 0    H₀: β₀ ≠ 0
H_a: β₀ = 0H₀: β₀ = 0
H_a: β₀ ≠ 0H₀: β₁ ≠ 0
H_a: β₁ = 0

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Do not reject H₀. We conclude that the relationship between price ($) and overall score is significant.Reject H₀. We conclude that the relationship between price ($) and overall score is significant.     Do not reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.Reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.

(b)

Test for a significant relationship using the F test. Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ = 0
H_a: β₁ ≠ 0H₀: β₁ ≠ 0
H_a: β₁ = 0    H₀: β₁ ≥ 0
H_a: β₁ < 0H₀: β₀ ≠ 0
H_a: β₀ = 0H₀: β₀ = 0
H_a: β₀ ≠ 0

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

What is your conclusion?

Do not reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.Do not reject H₀. We conclude that the relationship between price ($) and overall score is significant.    Reject H₀. We conclude that the relationship between price ($) and overall score is significant.Reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.

(c)

Show the ANOVA table for these data. (Round your p-value to three decimal places and all other values to two decimal places.)

you may need to use the appropriate technology to answer this question.

Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest).

(a) The estimated regression equation for this data is  ŷ = 26.268 + 0.297x,  where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use α = 0.05.

State the null and alternative hypotheses.

State the null and alternative hypotheses.

H₀: β₀ = 0
H_a: β₀ ≠ 0H₀: β₁ = 0
H_a: β₁ ≠ 0    H₀: β₁ ≥ 0
H_a: β₁ < 0H₀: β₁ ≠ 0
H_a: β₁ = 0H₀: β₀ ≠ 0
H_a: β₀ = 0

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Reject H₀. We conclude that the relationship between price ($) and overall score is significant.Reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.     Do not reject H₀. We conclude that the relationship between price ($) and overall score is significant.Do not reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.

(b)

Test for a significant relationship using the F test. Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₀ ≠ 0
H_a: β₀ = 0H₀: β₀ = 0
H_a: β₀ ≠ 0    H₀: β₁ = 0
H_a: β₁ ≠ 0H₀: β₁ ≥ 0
H_a: β₁ < 0H₀: β₁ ≠ 0
H_a: β₁ = 0

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

What is your conclusion?

A) Reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.

B) Do not reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.   

C) Do not reject H₀. We conclude that the relationship between price ($) and overall score is significant

D) Reject H₀. We conclude that the relationship between price ($) and overall score is significant.

(c)Show the ANOVA table for these data. (Round your p-value to three decimal places and all other values to two decimal places.)

Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest).

1. The estimated regression equation for this data is  ŷ = 21.990 + 0.330x, where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use α = 0.05.

1a. State the null and alternative hypotheses.

(a) H₀: β₀ ≠ 0
H_a: β₀ = 0

(b) H₀: β₁ = 0
H_a: β₁ ≠ 0    

(c) H₀: β₁ ≠ 0
H_a: β₁ = 0

(d) H₀: β₀ = 0
H_a: β₀ ≠ 0

(e) H₀: β₁ ≥ 0
H_a: β₁ < 0

1b. Find the value of the test statistic. (Round your answer to three decimal places.)

1c. Find the p-value. (Round your answer to four decimal places.)

p-value =

1d. What is your conclusion?

(a) Do not reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.

(b) Reject H₀. We conclude that the relationship between price ($) and overall score is significant.     

(c) Reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.

(d) Do not reject H₀. We conclude that the relationship between price ($) and overall score is significant.

2. Test for a significant relationship using the F test. Use α = 0.05.

2a. State the null and alternative hypotheses.

(a) H₀: β₁ = 0
H_a: β₁ ≠ 0

(b) H₀: β₀ = 0
H_a: β₀ ≠ 0    

(c) H₀: β₁ ≠ 0
H_a: β₁ = 0

(d) H₀: β₀ ≠ 0
H_a: β₀ = 0

(e) H₀: β₁ ≥ 0
H_a: β₁ < 0

2b. Find the value of the test statistic. (Round your answer to two decimal places.)

2c. Find the p-value. (Round your answer to three decimal places.)

p-value =

2d. What is your conclusion?

(a) Do not reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.

(b) Reject H₀. We conclude that the relationship between price ($) and overall score is significant.    

(c) Reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.

(d) Do not reject H₀. We conclude that the relationship between price ($) and overall score is significant.

3,. Show the ANOVA table for these data. (Round your p-value to three decimal places and all other values to two decimal places.)

SHOW STEPS IN EXCEL PLEASE

Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest).

(a)

The estimated regression equation for this data is

ŷ = 22.726 + 0.323x,

where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ = 0
H_a: β₁ ≠ 0H₀: β₀ = 0
H_a: β₀ ≠ 0    H₀: β₁ ≠ 0
H_a: β₁ = 0H₀: β₀ ≠ 0
H_a: β₀ = 0H₀: β₁ ≥ 0
H_a: β₁ < 0

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Do not reject H₀. We conclude that the relationship between price ($) and overall score is significant.Reject H₀. We conclude that the relationship between price ($) and overall score is significant.     Reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.Do not reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.

(b)

Test for a significant relationship using the F test. Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ = 0
H_a: β₁ ≠ 0H₀: β₀ ≠ 0
H_a: β₀ = 0    H₀: β₁ ≥ 0
H_a: β₁ < 0H₀: β₀ = 0
H_a: β₀ ≠ 0H₀: β₁ ≠ 0
H_a: β₁ = 0

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

What is your conclusion?

Do not reject H₀. We conclude that the relationship between price ($) and overall score is significant.Reject H₀. We conclude that the relationship between price ($) and overall score is significant.     Reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.Do not reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.

(c)

Show the ANOVA table for these data. (Round your p-value to three decimal places and all other values to two decimal places.)

To do this in C++ preferably not in a class but if not possible do in a class.

Assignment Specifications

Your assignment is to write a single-player version of the casino card game Blackjack, also known as 21. The goal of the game Blackjack is to get cards whose total value comes closest to 21 without going over. Getting a card total over 21 is called "busting". The player will play against the dealer. There are 3 possible outcomes.

• Player comes closer to 21 than the dealer or the dealer busts but the player did not bust -> player wins the bet amount.

• The dealer comes closer to 21 than the player or the player's total exceeds 21 -> player loses. Note if both the player and the dealer bust, then the dealer wins. This is called the "house advantage".

• Both player and dealer have the same total and neither player busts -> tie, no money is exchanged.

At each round of play, the player will be asked to enter their bet. They will then be given 2 cards. The player will repeatedly be asked if they want to draw another card. The player can continue to draw cards while their total is less than 21. After the player's turn is over, the dealer's cards are shown. The dealer's play is always the same: the dealer will continue to draw cards if their total is less than or equal to 16.

A sample run is shown below. Assume the player starts with $100 and the game ends when the player is down to $0 or their amount exceeds $1,000. Also note the user is prompted to re-enter their bet amount if they try to bet more than they actually have.

Programming instructions

Your program should have a function called draw_card that draws a random card. The function should get a random number between 1 and 13 to determine the rank of the card and another number between 1 and 4 to determine the suite of the card. The card of rank 13 corresponds to a king, the card of rank 12 corresponds to a queen, the card of rank 11 corresponds to a jack and card of rank 1 is an ace. In blackjack face cards (Jack, Queen, King) all count as 10 points towards the card total. The function should return the value of the card to be added to the point total. Aces can be either 11 (high) or 1 (low), depending on which is more advantageous to the player to come closest to 21 without going over. The card variable will contain the description of the card such as "Two of diamonds" or "King of hearts".

You should also have a getSuit and getRank function that takes as input an int that corresponds to a Rank or Suit and returns the string version of that rank or suit. For example, rank 10 would have to return “Jack”. Suit 3 would return “hearts”.

Note: Your rand values should have spades = 0, clubs = 1, diamonds = 2, and hearts = 3.

You should seed srand(333)

Note: In your main you should have a variable that keeps track of the current total for the player and another variable that keeps track of the current total for the dealer. When the draw card function is called you should pass to it a string variable called card and the current total. Your function draw_card will return the value of the card it draws and this value should be added in main to the current total. Note that the total is only used in this function to decide if ace should count as high or low. This function does not return the total! It returns the value of the card that was drawn. You are responsible for adding this value to the total in main. When you call the function draw_card you will also pass it a string called card. After calling the function draw_card this variable card will now have the description of the card, something like "Three of diamonds". Do not output anything in the function draw card! All output should be done in main.

//-------------------------------------------------------------------

// draw_card()

// Uses rand() to draw a card then returns the numerical

// value and card name

//-------------------------------------------------------------------

int draw_card(string &card, //IN - card name

               int drawer_points); //IN - drawer's total points

/****************************************************************

*

* draw_card()

*_______________________________________________________________

* Simulates the drawing of a card. Passes by reference the

* kind of card (value and suite in string value) as well as

* returns the card's equivalent numerical value (to be added

* to totals in main())

* Also reads current drawer's points to determind value of

* aces

*_______________________________________________________________

* PRE-CONDITIONS:

* &card : passes card info

* drawer_points : reads current drawer's points to determine

* value of ace

*

* POST-CONDITIONS:

* passes card info by reference, returns card numerical value

****************************************************************/

int draw_card (string &card, //card info

                int drawer_points) //current drawer's points

Note: You do not need to account for cases where you draw a 3 and then an Ace giving you a total of 14 (Ace counts here as 11) and then you draw a Queen giving you a total of 24. In real Blackjack you would now revert the Ace back to 1 giving you a total of 14. However, this is too complicated and we will not deal with this issue. Once Ace has been counted as 11 it will stay as 11.

Things to test for:

• Player busts

• Dealer busts

• Player loses all his money (Game Over)

• Player wins (total is more than $1000)

• Program halts when appropriate

FAQ

Q: Can the same card come up multiple times?

A: Yes. We will assume that the dealer uses multiple decks so for instance a four of clubs can come up many times in the same hand.?

Q: What happens if the player gets 21 does he automatically win?

A: In real blackjack rules the dealer gets to draw even if the player has gotten a 21. If the dealer also gets a 21 then it is considered a draw.

Example Run

You have $100. Enter bet:

50

Your cards are:

  Ten of Clubs

  Ace of Spades

The dealer's cards are:

  King of Hearts

  Seven of Clubs

The dealer's total is 17.

You win $50.

Play again? (y/n):

y

You have $150. Enter bet:

50

Your cards are:

  Seven of Clubs

  Jack of Hearts

Your total is 17. Do you want another card (y/n)?

n

The dealer's cards are:

  Queen of Spades

  Two of Diamonds

The dealer's total is 12.

The dealer draws a card.

  Five of Diamonds

The dealer's total is 17.

A draw! You get back your $50.

Play again? (y/n):

y

You have $150. Enter bet:

50

Your cards are:

  Nine of Clubs

  Queen of Spades

Your total is 19. Do you want another card (y/n)?

y

You draw a:

  Five of Clubs

Your total is 24. You busted!

Play again? (y/n):

y

You have $100. Enter bet:

100

Your cards are:

  Ace of Spades

  Three of Diamonds

Your total is 14. Do you want another card (y/n)?

y

You draw a:

  Eight of Hearts

Your total is 22. You busted!

You have $0. GAME OVER.

Example

The dealer's cards are:

  Two of Clubs

  Four of Diamonds

The dealer's total is 6.

The dealer draws a card.

  Three of Hearts

The dealer draws a card.

  Two of Clubs

The dealer draws a card.

  Nine of Spades

The dealer's total is 20.

Too bad. You lose $40.